Question

A cube painted yellow on all faces is cut into 27 small cubes of equal size. How many cubes are not painted on any side?
Options are a) 1
b) 6
c) 8
d) 12

Answer 1

It will be cut into a 3x3x3.
The cubes that are not painted will not be at the surface.
Lets first count the cubes at the surface.
It will be 9 in the front and the back = 18
3 on each side remaining as the other 6 on each side are already taken into account.
1 on the top and the bottom as the rest have already been taken
No. of painted cubes = 18 + 6 + 2 = 26
N. of cubes not painted = 27 - 26 = 1
Thus, the ans is a